Freshness inventory refers to a stocking system of products with a relatively short shelf life such that managing some measure of freshness is a central concern. Freshness inventory differs from perishable inventory in several ways. Perishable inventory has a binary (0-1) utility: zero utility after the expiration date and full utility before. The utility of freshness inventory, in contrast, dynamically decreases to zero over time. Control of perishable inventory involves the usual tracking of on-hand inventory, in terms of quantities, along with the replenishment decisions: when to order and how much to order. A popular replenishment policy is the single critical-number policy—comparing the total on-hand inventory with the base-stock level, which is the critical number, and order up to the latter.
The existing research on perishable inventory mostly focuses on stationary models, where products have either fixed or random shelf-life. For a single product with a fixed lifetime under periodic review, the optimal policy is identified in Fries (Fries, S. 1975. Optimal order policies for a perishable commodity with fixed lifetime. 1975. Oper. Res. 23, 46-61) and Nahmias (Nahmias, S. 1975. Optimal ordering policies for perishable inventory-II. Oper. Res. 23, 735-749), via dynamic programming, in terms of the order quantities as a function of the age distribution of the on-hand inventory. The optimal order quantities, being solutions to functional equations, are usually difficult to evaluate. Approximations are proposed, which often take the form of a “critical number” (i.e., order-up-to) policy, where the critical number is either optimized or approximated (Cohen, M. A. 1976. Analysis of single critical number ordering policies for perishable inventories. Oper. Res. 24, 726-741; Nahmias), or a policy with a fixed order quantity (Brodheim, E. C., C. Derman and G. P. Prastacos. 1975. On the evaluation of a class of inventory policies for perishable products such as whole blood. Mgmt. Sci. 21, 1320-1325). Cooper (Cooper, W. L. 2001. Pathwise properties and performance bounds for a perishable inventory system. 2001. Oper. Res. 49(3) 455-466.) considers the critical-number policy and derive bounds on the stationary distribution of the number of perished/discarded units (“outdates”) by the end of each period. The bounds are useful to identify the right critical number to use while meeting a required level of quality-of-service.
Under Poisson demand, zero lead time and fixed product lifetime, Weiss (Weiss, H. J. 1980. Optimal ordering policies for continuous review perishable inventory models. Oper. Res. 28, 365-374) shows that under continuous review, the optimal policy is (S, s), with s=0 in the lost sales case. Liu and Lian (Liu, L., Z. Lian. 1999. (s, S) continuous review models for products with fixed lifetimes. 1999. Oper. Res. 47, 150-158) consider the same (S, s) policy, under renewal demand, and derive closed-form results for the steady-state inventory distribution in the case of backordering. In a recent study, Cai et al. (Cai, X., J. Chen, Y. Xiao, X. Xu. 2009. Optimization and coordination of fresh product supply chains with freshness-keeping effort. Prod. Oper. Mgmt. 19, 261-278), a freshness index and a surviving index are developed to measure the quality and the quantity of the stock available to supply the demand; and decisions are made via a single-period newsvendor-like model, on the order quantity, selling price, and the level of freshness-keeping effort involved in shipping the product to the market.